Channel estimation by phase multiplexed complementary sequences

ABSTRACT

The present invention relates to a method of estimating a transmission or telecommunications channel in which method a composite signal of complementary sequences such as:  
     φ s,s ( n )+φ g,g ( n )= k. δ( n )  ( 1 )  
     is used.  
     According to the present invention, said method is characterised in that a pair of complementary sequences s(n) and g(n) is transmitted after having multiplexed them in phase.

[0001] The present invention relates to a method of estimating atransmission or telecommunications channel which uses complementarysequences. The method results either in obtaining an optimal estimationof the phase and of the attenuation in the case of a single-path channelif the arrival time of the signal is known, or in obtaining a veryeffective estimation of the delays, phases and attenuations of thedifferent paths in the case of a multipath channel. The method alsomakes it possible to obtain an estimation in the case of a channel ofwhich it is not possible to distinguish the different paths or in thecase of a multipath channel, of which one of the paths is very powerfulin comparison with all the others, as long as the arrival time of thesignal is known.

[0002] In a telecommunications system, information circulates betweentransmitters and receivers through-channels. In this connection, FIG. 1illustrates a model, which is discrete in time, of the transmissionchain between a transmitter 1 and a receiver 2 through a transmissionchannel 3. As a general rule, the transmission channels can correspondto different physical, radio, wire, optical media etc., and to differentenvironments, fixed or mobile communications, satellites, submarinecables, etc.

[0003] As a result of the multiple reflections of which the wavesemitted by transmitter 1 can be the object, channel 3 is a multipathchannel which is generally modelled as FIG. 1 indicates. It is thenconsidered to be a shift register 30 comprising L serial cells (referredto by a subscript k able to take values of between 1 and L) and thecontents of which are shifted towards the right of FIG. 1 each time asymbol arrives at its input. The output of each cell with the subscriptk is applied to a filter 31 representing the interference undergone bythis output and introducing an attenuation of the amplitude α_(k), aphase shift α_(k) and a delay r_(k). The outputs of the filters aresummed in a summer 32. The total impulse response thus obtained ismarked h(n).

[0004] The output of summer 32 is applied to the input of an adder 33which receives, moreover, a random signal, modelled by a Gaussian whitenoise, ω(n) which corresponds to the thermal noise which is present inthe telecommunications system. In FIG. 1, the reference h(n) has beenused, in channel 3, for the register 30, the filters 32 and the summer33, followed by an adder which adds the noise ω(n).

[0005] It will be understood that, if the transmitter 1 transmits thesignal e(n), the signal received r(n), in the receiver 2, is thus:$\begin{matrix}{{r(n)} = {{{e(n)}*{h(n)}} + {w(n)}}} \\{= {{{e(n)}*{\sum\limits_{k = 1}^{L}{a_{k}{\delta \left( {n - r_{k}} \right)}^{j\quad a_{k}}}}} + {w(n)}}} \\{= {{\sum\limits_{k = 1}^{L}{a_{k}{e\left( {n - r_{k}} \right)}^{j\quad a_{k}}}} + {w(n)}}}\end{matrix}$

[0006] In these expressions${h(n)} = {\sum\limits_{k = 1}^{L}{a_{k}{\delta \left( {n - r_{k}} \right)}^{{j\alpha}_{k}}}}$

[0007] denotes the impulse response of the channel, δ(n) being the Diracimpulse. The operator * denotes the convolution product, defined by thefollowing relation:${c(n)} = {{{a(n)}*{b(n)}} = {\sum\limits_{m = {- \infty}}^{+ \infty}{{a(m)} \cdot {b\left( {n - m} \right)}}}}$

[0008] Thus it is generally necessary to determine the characteristicsof channel 3, at a given moment, in order to thwart the induceddistortion of the transmitted signal e(n). In order to obtain anestimation of h(n), i.e. of the coefficients α_(k), r_(k) and α_(k) ofthe model of channel 3, it is necessary to repeat this operation at agreater or lesser frequency depending on the rate at which thecharacteristics of the channel evolve.

[0009] A widespread method of estimating the channel consists intransmitting, via transmitter 1, signals e(n) which are predeterminedand known-to receiver 2, and in comparing the signals received r(n) inreceiver 2, by means of a periodic or aperiodic correlation, with thosewhich are expected there in order to deduce from them thecharacteristics of the channel. The aperiodic correlation of two signalsof length N has a total length 2N-1 and is expressed, from theconvolution product, by the relation:${{{\phi_{a,b}(n)}{a^{*}\left( {- n} \right)}*{b(n)}} = {\sum\limits_{m = 0}^{N - 1}{{a(m)} \cdot \left( {b\left( {m + n} \right)} \right)^{(1)}}}},{\lbrack m\rbrack = 0},1,\ldots \quad,{N - 1}$

[0010] for two signals α(n) and h(n) of finite length N, where theoperator * denotes the complex conjugate operation.

[0011] The correlation of the received signal r(n) with the knowntransmitted signal e(n) translates as:

r(n)*e ^(*)(−n)=[e(n)*h(n)+ω(n)]*e ^(*)(−n)

φ_(e,r)(n)=φ_(e,e*h)(n)+φ_(e,w)(n)

=φ_(e,e)(n)*h(n)+φ_(e,w)(n)

[0012] The result of the correlation operation constitutes theestimation of the impulse response of the channel: the quality or theprecision of the estimation is aUl the better if φ_(e,r)(n) tendstowards h(n). The latter is directly dependant on the choice oftransmitted sequence e(n); to optimise the estimation process, thesignal e(n) should be chosen in such a way that φ_(e,e)(n) tends towardsk.δ(n), k being a real number, and that φ_(e,ω)(n)/φ_(e,e)(n) tendstowards O. In fact, in this case, the estimation of the channel becomes:

φ_(e,r)(n)=k.δ(n)*h(n)+φ_(e,ω)(n)

=k.h(n)+φ_(e,ω)(n)

φ_(e,r)(n)≈k.h(n)

[0013] It has been demonstrated that no single sequence exists for whichthe function of aperiodic auto-correlation is equal to φ_(e,e)(n),k,δ(n).

[0014] One object of the present invention consists in using pairs ofcomplementary sequences which have the property that the sum of theirauto-correlations is a perfect Dirac function. Let s(n) and g(n), n=0,1,. . . , N−1 be a pair of complementary sequences:

φ_(s,s)(n)+φ_(g,g)(n)=k.δ(n)  (1)

[0015] Several methods of constructing such complementary sequences areknown in the literature: Golay complementary sequences, polyphasecomplementary sequences, Welti sequences, etc. By way of information,one will be able to refer, in this connection, to the followingtechnical documents which deal with the introduction to complementarysequences and, in particular, to Golay complementary sequences as wellas to a Golay correlator:

[0016] 1) “On aperiodic and periodic complementary sequences” by FengK., Shiue P. J. -S., and Xiang Q., published in the technical journalIEEE Transactions on Information Theory, Vol. 45, no. 1, January 1999,

[0017] 2) “Korrelationssignale” by Lüke H. -D, published in thetechnical journal ISBN 3-540-545794, Springer-Verlag Heidelberg NewYork, 1992,

[0018] 3) “Polypbase Complementary Codes” by R. L. Frank, published inthe technical journal IEEE Transactions on Information Theory, November1980, Vol. IT26, no. 6,

[0019] 4) “Multiphase Complementary Codes” by R. Sivaswamy, published inthe technical journal IEEE Transactions on Information Theory, September1978, Vol. IT-24, no. 5,

[0020] 5) “Efficient pulse compressor for Golay complementary sequences”by S. Z. Budissin, published in the technical journal ElectronicsLetters, Vol. 27, no. 3, January 1991,

[0021] 6) “Complementary Series” by M. J. Golay, published in thetechnical journal IRE Trans; on Information Theory”Vol. IT-7, April1961,

[0022] 7) “Efficient Golay Correlator” by B. M. Popovic, published inthe technical journal IEEE Electronics Letters, Vol. 35, no. 17, August1999.

[0023] Reference can also be made to the descriptions of the documentsU.S. Pat. Nos. 3,800,248, 4,743,753, 4,968,880, 5,729,612, 5,841,813,5,862,182 and 5,961,463.

[0024] The property of complementary sequences in having a perfect sumof autocorrelations is illustrated in FIG. 2, taking, by way of example,a pair of Golay complementary sequences of length N=16 bits.

[0025] In FIG. 2 are plotted on the x-co-ordinates the time shifts inrelation to perfect synchronisation. The possible shifts are numberedfrom 1 to 31 for the pair of sequences s(n) and g(n), and on they-co-ordinates the correlations from −5 to +35. The curve in dashescorresponds to the auto-correlation φ_(s,s)(n) of the sequence s(n); thecurve in a dot-dash line to the auto-correlation φ_(g,g)(n) of thesequence g(n): and the curve in an unbroken line to the sum of theauto-correlations φ_(s,s)(n) and φ_(g,g)(n). One can see that the curvein an unbroken line merges with the axis of the x-co-ordinates betweenpoints 0 and 15 and points 17 and 31, but it corresponds practically toa Dirac fimction between points 15 to 17.

[0026] The theoretically perfect auto-correlation properties of thesecomplementary sequences may, however, only be exploited if theirtransmission can be ensured in such a manner that the occurrence ofinter-correlations φ_(s,g)(n) and /or φ_(g,s)(n) is avoided.

[0027] According to one feature of the invention, a method is providedof estimating a transmission or telecommunications channel, in whichmethod a composite signal of complementary sequences is used and inwhich a pair of complementary sequences s(n) and g(n) is transmittedafter having multiplexed them in phase.

[0028] According to another feature of the invention, a method isprovided of constructing the composite signal from a pair of polyphasecomplementary sequences s(n) and g(n) which are multiplexed in phase,this method making it possible to exploit the propertyφ_(s,s)(n)+φ_(g,g)(n) mentioned in the relation (1) above.

[0029] According to another feature, the composite signal is made up oftwo polyphase complementary sequences s(n) and (g(n) transmitted with aphase shift between them of 90°, i.e. the transmitted composite signale(n) is in the form of the relation (2) below:

[0030]   e(n)=e ^(iφ).(s(n)+j.g(n))  (2)

[0031] with an initial, fixed and known phase shift φ.

[0032] In the case of binary complementary sequences s(n) and g(n), witha number of phases P equal to 2, i.e. the case of Golay complementarysequences, the transmitted signal e(n) is in the form of a signal2P-PSK, or 4-PSK, as FIG. 3 shows in the complex plane. FIG. 3represents, id the complex plane (R,I), the transmitted composite signale(n), of which the values 0 or 1 taken by each component s(n), g(n) arerespectively represented by the ends of a corresponding segment S and G.Segments S and G are out of phase with one another by II/2.

[0033] In the more general case of polyphase complementary sequenceswith a number of phases P greater than 2, the transmitted signal e(n)takes the form of a signal (2P)-PSK.

[0034] According to another feature, a device is provided which isintended to generate the composite signal according to relation (2) andwhich comprises a first generator capable of generating the firstsequence s(n), with n varying from 0 to N-1, the output of which isconnected to the first input of an adder, and a second generator capableof generating the second sequence g(n), with n varying from 0 to N-1,the output of which is connected to the input of a first circuitshifting phase by 90°, the output of which is connected to the secondinput of the adder, the output of the adder being connected to the inputof a second circuit shifting phase by φ which delivers the compositesignal.

[0035] The features of the present invention mentioned above, as well asothers, will appear more clearly in reading the description ofembodiments, said description being made in connection with the attacheddrawings, amongst which:

[0036]FIG. 1 is a known diagram of a discrete model of a transmissionchannel,

[0037]FIG. 2 is a known curve illustrating the auto-correlation of twoGolay complementary sequences and the sum of their auto-correlations,

[0038]FIG. 3 illustrates a method of multiplexing in phase twocomplementary sequences, according to the invention,

[0039]FIG. 4 is the diagram of an embodiment of the device provided togenerate the composite sequence of the invention,

[0040]FIG. 5 is a block diagram showing a circuit for processing bycorrelation, connected in series with a device for estimating thechannel, the processing circuit receiving the signal r(n),

[0041]FIG. 6 is a block diagram showing an embodiment of a device forsingle-path channel estimation, and

[0042]FIG. 7 is a block diagram showing another embodiment of a devicefor multipath channel estimation.

[0043] The device shown in FIG. 4 is intended to produce the compositesignal according to relation (2), i.e.

e(n)=e ^(jφ).(s(n) j.g(n))  (2)

[0044] This device comprises a first generator 4 capable of generatingthe first sequence s(n), with n varying from 0 to N-1, the output ofwhich is connected to the first input of an adder 5, and a secondgenerator 6 capable of generating the second sequence g(n), with nvarying from 0 to N-1, the output of which is connected to the input ofa first phase-shifting circuit, 7, supplying a phase shift of 90°, theoutput of which is connected to the second input of the adder 5, theoutput of the adder 5 being connected to the input of a secondphase-shifling circuit 8 which supplies the phase shift φ and whichdelivers the composite signal e(n).

[0045]FIG. 5 shows the general structure of a signal processing circuit9, to the input of which is applied the signal r(n) received in thereceiver 2, FIG. 1, coming from the transmission channel 3.

[0046] Passing into a multipath channel, the total impulse response ofwhich is:${h(n)} = {\sum\limits_{k = 1}^{L}{a_{k}\delta \quad \left( {n - r_{k}} \right)^{j\quad a_{k}}}}$

[0047] the received signal r(n) becomes: $\begin{matrix}{{r(n)} = {\sum\limits_{k = 1}^{L}{a_{k} \cdot ^{j\quad a_{k}} \cdot {e\left( {n - r_{k}} \right)}}}} \\{= {\sum\limits_{k = 1}^{L}{a_{k} \cdot ^{j \cdot {({a_{k} + \varphi})}} \cdot \left( {{s\left( {n - r_{k}} \right)} + {j \cdot {g\left( {n - r_{k}} \right)}}} \right)}}} \\{= {{r_{I}(n)} + {k \cdot {r_{Q}(n)}}}}\end{matrix}$

[0048] The real and imaginary parts of the received signal r(n) areexpressed in the following manner: $\begin{matrix}{\begin{matrix}{{r_{I}(n)} = \quad {{Re}\left\{ {\sum\limits_{k = 1}^{L}{a_{k} \cdot \left( {{\cos \quad \left( {\alpha_{k} + \varphi} \right)} + {j \cdot {\sin \left( {\alpha_{k} + \varphi} \right)}}} \right) \cdot}} \right.}} \\{\quad \left. \left( {{s\left( {n - r_{k}} \right)} + {j \cdot {g\left( {n - r_{k}} \right)}}} \right) \right\}} \\{= \quad {\sum\limits_{k = 1}^{L}\left( {{{a_{k} \cdot \cos}\quad {\left( {\alpha_{k} + \varphi} \right) \cdot {s\left( {n - r_{k}} \right)}}} - {a_{k} \cdot}} \right.}} \\{\quad \left. {{\sin \left( {\alpha_{k} + \varphi} \right)} \cdot {g\left( {n - r_{k}} \right)}} \right)}\end{matrix}\begin{matrix}{{r_{Q}(n)} = \quad {{Im}\left\{ {\sum\limits_{k = 1}^{L}{a_{k} \cdot \left( {{\cos \quad \left( {\alpha_{k} + \varphi} \right)} + {j \cdot {\sin \left( {\alpha_{k} + \varphi} \right)}}} \right) \cdot}} \right.}} \\{\quad \left. \left( {{s\left( {n - r_{k}} \right)} + {j \cdot {g\left( {n - r_{k}} \right)}}} \right) \right\}} \\{= \quad {\sum\limits_{k = 1}^{L}\left( {{{a_{k} \cdot \cos}\quad {\left( {\alpha_{k} + \varphi} \right) \cdot {s\left( {n - r_{k}} \right)}}} + {a_{k} \cdot}} \right.}} \\{\quad \left. {{\cos \left( {\alpha_{k} + \varphi} \right)} \cdot {g\left( {n - r_{k}} \right)}} \right)}\end{matrix}} & (3)\end{matrix}$

[0049] The processing circuit 9 is made up of two correlators 10 and 11and an estimation device 12. The input of the processing circuit 9receives the signal r(n) and applies the real part r₁(n) to correlator10 which proceeds separately to correlation with the two sequences s(n)and g(n), and the imaginary part r_(Q)(n) to correlator 11 whichproceeds likewise to correlation with the two sequences s(n) and g(n),

[0050] Thus, at the respective outputs of correlators IO and 11, signalsare obtained which contain the contributions of the auto-correlations ofs(n) and g(n), and the contributions of their inter-correlations, andwhich are mentioned below:${c_{I}^{s}(n)} = {\sum\limits_{k = 1}^{L}\left( {{a_{k} \cdot {\cos \left( {\alpha_{k} + \varphi} \right)} \cdot {\phi_{s,s}\left( {n - r_{k}} \right)}} - {a_{k} \cdot {\sin \left( {\alpha_{k} + \varphi} \right)} \cdot {\phi_{g,s}\left( {n - r_{k}} \right)}}} \right)}$

$\begin{matrix}{\begin{matrix}{{c_{I}^{g}(n)} = \quad {\sum\limits_{k = 1}^{L}\left( {{{a_{k} \cdot \cos}\quad {\left( {\alpha_{k} + \varphi} \right) \cdot {\phi_{s,g}\left( {n - r_{k}} \right)}}} - {a_{k} \cdot}} \right.}} \\{\quad \left. {{\sin \left( {\alpha_{k} + \varphi} \right)} \cdot {\phi_{g,g}\left( {n - r_{k}} \right)}} \right)}\end{matrix}\begin{matrix}{{c_{Q}^{s}(n)} = \quad {\sum\limits_{k = 1}^{L}\left( {{{a_{k} \cdot \sin}\quad {\left( {\alpha_{k} + \varphi} \right) \cdot {\phi_{s,g}\left( {n - r_{k}} \right)}}} + {a_{k} \cdot}} \right.}} \\{\quad \left. {{\cos \left( {\alpha_{k} + \varphi} \right)} \cdot {\phi_{g,s}\left( {n - r_{k}} \right)}} \right)}\end{matrix}\begin{matrix}{{c_{Q}^{g}(n)} = \quad {\sum\limits_{k = 1}^{L}\left( {{{a_{k} \cdot \sin}\quad {\left( {\alpha_{k} + \varphi} \right) \cdot {\phi_{s,g}\left( {n - r_{k}} \right)}}} + {a_{k} \cdot}} \right.}} \\{\quad \left. {{\cos \left( {\alpha_{k} + \varphi} \right)} \cdot {\phi_{g,g}\left( {n - r_{k}} \right)}} \right)}\end{matrix}} & (4)\end{matrix}$

[0051] of which the two first c₁ ^(s)(n) and c₁ ⁸(ii) are delivered bycorrelator 10, and the last two c_(Q) ^(s)(n) and c_(Q) ^(s)(n) aredelivered by correlator 11. These four signals are applied to theestimation device 12.

[0052] In a first case, that of device 12 of FIG. 6, it was consideredthat the transmission channel 3 of FIG. 1 was a single-path channel oreven a multipath transmission channel, of which it is not possible todistinguish the different paths, or a multipath channel, of which one ofthe paths is very powerful in comparison with all the other paths. Inthis case, the coefficient L used in the relation of the preamble:$\begin{matrix}{{r(n)} = {{{e(n)}*{h(n)}} + {w(n)}}} \\{= {{{e(n)}*{\sum\limits_{k = 1}^{L}{a_{k}{\delta \left( {n - r_{k}} \right)}^{j\quad a_{k}}}}} + {w(n)}}} \\{= {{\sum\limits_{k = 1}^{L}{a_{k}{e\left( {n - r_{k}} \right)}^{j\quad a_{k}}}} + {w(n)}}}\end{matrix}$

[0053] is equal to one, and if the arrival time r₁ is known, thecorrelation values obtained by the above relations (4) can be combinedin a simple manner, which makes it possible to determine α₁ and α₁ viathe estimation device 12 shown in FIG. 6.

[0054] The estimation device of FIG. 6 comprises four memories FiFo 13to 16, memory 13 receiving the signal c₁ ^(s)(n), memory 14 the signalc₁ ^(g)(n), memory 15 the signal c_(Q) ^(s)(n) and memory 16 the signalc_(Q) ^(g)(n). For each of these signals, all the 2N -1 correlationvalues centred on the known arrival time of the signal r(n) arecalculated and saved in memory. The outputs of memories 13 and 16 arerespectively connected to the two inputs of an adder circuit 17, whilstthe outputs of memories 14 and 15 are respectively connected to the twoinputs of a subtracter circuit 18. The output of circuit 17 delivers thesignal w₁, whilst the output of circuit 18 delivers the signal ω₂. Thesetwo signals are applied to a circuit 19 for calculating α and α.

[0055] In calculating the signals ω₁ and ω₂ as the relations (5)indicate below:

ω₁(m)=(c ₁ ^(s)(−m))^(*) +c _(Q) ^(g)(m)

=a ₁. cos (α₁+Φ).((φ_(s,s)(−m))^(*)+φ_(g,g)(m))+α₁. sin(α₁+φ).(φ_(s,g)(m)−(φ_(g,s)(−m))^(*))

ω₂=(m)=(c _(Q) ^(s)(m))^(*) −c ₁ ^(g)(−m)

=α₁. sin (α₁+Φ).(φ_(s,s)(m)+(φ_(g,g)(−m))^(*))+α₁. cos(α₁+φ).(φ_(g,s)(m)−(φ_(s,g)(−m))^(*))  (5)

[0056] where m=-N+1, -N+2, . . . N−2, N−1 is chosen as the index for thecorrelation values calculated and saved in memory, in this order.

[0057] With the two following relations:

φ_(s,s)(m)=φ_(s,s) ^(*)(−m)

φ_(s,g)(m)=φ_(g,s) ^(*)(−m)

[0058] which are valid for all s(n) and g(n) sequences, equation (5) issimplified and one obtains:

ω₁(m)=α₁. cos (α₁+Φ).(φ_(s,s)(m)+φ_(g,g)(m))

ω₂(m)=α₁. sin (α₁+Φ).(φ_(s,s)(m)+φ_(g,g)(m))  (6)

[0059] These two signals are thus in the form of a Dirac weighted by thechannel coefficients, fvom which the attenuation and the phase shiftcain be obtained, in the calculating circuit 19, by the relations:$\alpha_{1} = {{\tan^{- 1}\left( \frac{w_{2}\left( {n - v} \right)}{w_{1}\left( {n - v} \right)} \right)} - \varphi}$$a = {{\frac{w_{1}\left( {n - v} \right)}{\cos \left( {\alpha_{1} + \varphi} \right)}\quad {or}\quad a} = \frac{w_{2}\left( {n - v} \right)}{\sin \left( {\alpha_{1} + \varphi} \right)}}$

[0060] with the initial known phase shift φ.

[0061] In the more general case shown in FIG. 7, the signals c₁ ^(s)(n),c_(l) ^(g)(n), c_(Q) ^(s)(n) and c_(Q) ^(s)(n) are applied respectivelyto the four inputs of a circuit 20 which calculates the differentcoefficients α_(k) and α_(k), determines r_(k) and delivers them to itsoutputs.

[0062] Indeed, in the case of a multipath transmission channel, it isnot possible to eliminate the inter-correlation terms which one had inthe relations (4) above. With an appropriate circuit 20, it isnevertheless possible to obtain estimations of coefficients of thetransmission channel.

[0063] Calculating from the equations (4), $\begin{matrix}{{w_{1}(n)} = {{c_{1}^{s}(n)} + {c_{Q}^{g}(n)}}} \\{= {\sum\limits_{k = 1}^{L}\begin{pmatrix}{{a_{k} \cdot {\cos \left( {\alpha_{k} + \varphi} \right)} \cdot \left( {{\phi_{s,s}\left( {n - r_{k}} \right)} + {\phi_{g,g}\left( {n - r_{k}} \right)}} \right)} -} \\{a_{k} \cdot {\sin \left( {\alpha_{k} + \varphi} \right)} \cdot \left( {{\phi_{s,g}\left( {n - r_{k}} \right)} - {\phi_{g,s}\left( {n - r_{k}} \right)}} \right)}\end{pmatrix}}}\end{matrix}$ $\begin{matrix}{{w_{2}(n)} = {{c_{Q}^{s}(n)} - {c_{1}^{g}(n)}}} \\{= {\sum\limits_{k = 1}^{L}\begin{pmatrix}{{a_{k} \cdot {\sin \left( {\alpha_{k} + \varphi} \right)} \cdot \left( {{\phi_{s,s}\left( {n - r_{k}} \right)} + {\phi_{g,g}\left( {n - r_{k}} \right)}} \right)} +} \\{a_{k} \cdot {\sin \left( {\alpha_{k} + \varphi} \right)} \cdot \left( {{\phi_{g,s}\left( {n - r_{k}} \right)} - {\phi_{s,g}\left( {n - r_{k}} \right)}} \right)}\end{pmatrix}}}\end{matrix}$

[0064] The two signals are in the formn of a Dirac weighted by thechannel coefficients plus other terms of inter-correlation between thecomplementary sequences s(n) and g(n).

[0065] With $\begin{matrix}{{z_{1}(n)} = {{w_{1}(n)} + {w_{2}(n)}}} \\{= {\sum\limits_{k = 1}^{L}\begin{pmatrix}{{a_{k} \cdot \left( {{\cos \left( {\alpha_{k} + \varphi} \right)} + {\sin \left( {\alpha_{k} + \varphi} \right)}} \right) \cdot \left( {{\phi_{s,s}\left( {n - r_{k}} \right)} + {\phi_{g,g}\left( {n - r_{k}} \right)}} \right)} +} \\{a_{k} \cdot \left( {{\sin \left( {\alpha_{k} + \varphi} \right)} - {\cos \left( {\alpha_{k} + \varphi} \right)}} \right) \cdot \left( {{\phi_{g,s}\left( {n - r_{k}} \right)} + {\phi_{s,g}\left( {n - r_{k}} \right)}} \right)}\end{pmatrix}}}\end{matrix}$ $\begin{matrix}{{z_{2}(n)} = {{w_{1}^{2}(n)} + {w_{2}^{2}(n)}}} \\{= {{a_{k}^{2} \cdot \left( {{\phi_{s,s}\left( {n - r_{k}} \right)} + {\phi_{g,g}\left( {n - r_{k}} \right)}} \right)^{2}} + {{secondary}\quad {terms}}}}\end{matrix}$

[0066] the delay r_(k) are d erived in an obvious manner and theattenuations and the phases can be determined by:$a_{k} = \frac{\sqrt{z_{2}(n)}}{2N}$$a_{k} = {- \left( {{\cos^{- 1}\left( \frac{z_{1}(n)}{2{\sqrt{2} \cdot N}} \right)} + \varphi - \frac{\Pi}{4}} \right)}$

1. Method of estimating a transmission or telecommunications channel, inwhich method a composite signal of complementary sequences such as:φ_(s,s)(n)+φ_(g,g)(n)=k.δ(n)  (1) is used, the method beingcharacterised in that a pair of complementary sequences s(n) and g(n) istransmitted after having multiplexed them in phase.
 2. Method ofestimating a transmission or telecommunications channel according toclaim 1 , characterised in that the composite signal is constructed froma pair of polyphase complementary sequences s(n) and g(n) which aremultiplexed in phase, this method making it possible to exploit theproperty φ_(s,s)(n)+φ_(g,g)(n) mentioned in the relation (1)mentioned-in claim 1 .
 3. Method of estimating a transmission ortelecommunications channel according to claim 1 , characterised in thatthe composite signal is made up of two polyphase complementary sequencess(n) and g(n), transmitted with a phase shift between them of 90°, i.e.the composite signal transmitted e(n) is in the form of the relation (2)below: e(n)=e ^(jφ).(s(n)+j.g(n))  (2) with an initial fixed and knownphase shift φ.
 4. Device intended to generate the composite signalaccording to relation (2) of claim 3 , to implement the method ofestimating a transmission or telecommunications channel according toclaim 1 , characterised in that it comprises a first generator (4)capable of generating the first sequence s(n), with n varying from 0 toN-1, the output of which is connected to the first input of an adder(5), and a second generator (6) capable of generating the secondsequence g(n), with n varying from 0 to N-1, the output of which isconnected to the input of a first circuit (7) shifting phase by 90°, theoutput of which is connected to the second input of the adder (5), theoutput of the adder (5) being connected to the input of a second circuit(8), shifting phase by φ and which delivers the composite signal e(n).5. Estimation device which receives the received signal r(n)corresponding to the composite signal according to claim 1 ,characterised in that it comprises a processing circuit (9) made up oftwo correlators (10 and 11) and an estimation device (12), the input ofthe processing circuit (9) receives the signal r(n) and applies the realpart of it r₁(n) to correlator (10), which proceeds simultaneously tocorrelation with the sequences s(n) and g(n), and applies the imaginarypart r_(Q)(n) to correlator (11), which likewise proceeds to correlationwith the two sequences s(n) and g(n).
 6. Estimation device according toclaim 5 , characterised in that said estimation device (12) comprisesfour memories FiFo (13 to 16), memory (13) receiving the signal c₁^(s)(n), memory (14) the signal c_(l) ^(g)(n), memory (15) the signalc_(Q) ^(s)(n) and memory (16) the signal c_(Q) ^(g)(n), the outputs ofmemories (13 and 16) being respectively connected to the two inputs ofan adder circuit (17), whilst the outputs of memories (14 and 15) arerespectively connected to the two inputs of a subtracter circuit (18),the output of circuit (17) delivering the signal ω₁, whilst the outputof circuit 18 delivers the signal w₂, these two signals being applied toa circuit (19) for calculating α and α.